The National Highway Traffic Safety Administration said last month it was investigating the 2011 Cruze because of two complaints of fires that engulfed the compact cars.
In documents posted on its website this week, regulators are asking GM for information about fires in 2011 and 2012 Cruzes.
Investigators are focusing on wiring and a computer that controls the transmission. They've asked GM for any allegations of overheated wiring or smoke and fire in the engine compartment.
GM spokesman Alan Adler says the investigation now covers about 370,000 cars. He says GM is co-operating. The car has not been recalled.
No one was hurt in the two fires reported to the government.